Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
The distance between the points (0, 0) and (36, 15) is 39 units. Yes, the distance between towns A and B is 39 km.
Explanation
This question directly applies the distance formula derived from Pythagoras Theorem. The numerical calculation tests if students can substitute coordinates correctly. The second part connects the abstract calculation to the real-world situation described in Section 7.2, where town B is located 36 km east and 15 km north of town A. Taking town A as origin (0,0), town B has coordinates (36, 15), making the mathematical distance equivalent to the actual distance between the towns.
Solution Steps
Step 1: Let the points be A(0, 0) and B(36, 15).
Step 2: Using the distance formula: Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 3: Substituting values: Distance = √[(36 - 0)² + (15 - 0)²] = √[36² + 15²]
Step 4: Calculating: Distance = √[1296 + 225] = = 39 units
Step 5: From Section 7.2, town B is located 36 km east and 15 km north of town A.
Step 6: Taking A as origin (0, 0), B has coordinates (36, 15).
Step 7: Therefore, distance between towns A and B = 39 km.